After going down 3-2, Edmonton would score two late goals to complete a rally of their own heading into Game 2, scheduled for April 22nd.
Oilers goaltender Connor Ingram earned his first career playoff win after saving 24 of Anaheim's 27 shots.
Recap & Highlights
Game 1 between the Oilers and Ducks became the only series to have a clean first period without a single penalty called.
Edmonon got things started thanks to a Jason Dickinson goal to go up 1-0 with under three minutes to go in the first.
It would take exactly one minute for the Oilers to double their lead before heading in for the first intermission.
Kasperi Kapanen would put the Oilers up 2-0, with an assist from Leon Draisaitl, who made his return to the ice after missing over a month due to injury.
Heading into the second, Edmonton had outshot Anaheim 14-4. But things would turn into a different story, and fast.
Just 17 seconds in, Troy Terry would slash the lead in half to 2-1 with his first goal of the playoffs.
It was the second-fastest goal to start a period in Ducks playoff history behind Samuel Pahlsson's 14-second goal during the 2007 Western Conference semi-finals.
And just like that, the rally began for Anaheim.
Leo Carlsson, who assisted on Terry's first goal, would find the net just four minutes later to tie it all up 2-2 for the Ducks.
The two would become just the second and third players in Ducks history to record multiple points in their playoff debut - the first was Paul Kariya in 1997.
Edmonton would have an opportunity to take the lead after Anaheim's Alex Killorn was called for tripping.
But the Oilers failed to convert on the power play, leaving the Ducks ready to take the lead of their own after they went on the power play eight minutes later.
Terry would score his second goal of the game to give Anaheim the 3-2 lead heading into the third, tying the franchise record for most goals in a playoff period.
After being dominated in the first period, the Ducks adjusted in the second, outshooting Edmonton 13-12.
In what was starting to look like an even-strength third period, the Oilers caught the Ducks' defensemen lacking as Dickinson would score his second of the game off a rebound to make it 3-3.
Edmonton would complete their own rally as Kapanen would also score his second of the game, which gave the Oilers a 4-3 lead with 1:49 left to go.
And, just like before, Draisaitl and Vasily Podkolzin would pick up their second assists on Kapanen's second goal en route to a Game 1 win, holding off one of the best late-game teams in the league.
Edmonton would finish the game outshooting (34-27) and outhitting (47-37) the Ducks.